-Convergence of Finite Element Approximation
J. A. Nitsche (1975)
Publications mathématiques et informatique de Rennes
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J. A. Nitsche (1975)
Publications mathématiques et informatique de Rennes
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Thomas L. Toulias (2013)
Discussiones Mathematicae Probability and Statistics
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A generalized form of the usual Lognormal distribution, denoted with , is introduced through the γ-order Normal distribution , with its p.d.f. defined into (0,+∞). The study of the c.d.f. of is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.
Péter Kórus, Ferenc Móricz (2009)
Studia Mathematica
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Let a single sine series (*) be given with nonnegative coefficients . If is a “mean value bounded variation sequence” (briefly, MVBVS), then a necessary and sufficient condition for the uniform convergence of series (*) is that as k → ∞. The class MVBVS includes all sequences monotonically decreasing to zero. These results are due to S. P. Zhou, P. Zhou and D. S. Yu. In this paper we extend them from single to double sine series (**) , even with complex coefficients . We also...
S. V. Konyagin, V. N. Temlyakov (2003)
Studia Mathematica
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We consider convergence of thresholding type approximations with regard to general complete minimal systems eₙ in a quasi-Banach space X. Thresholding approximations are defined as follows. Let eₙ* ⊂ X* be the conjugate (dual) system to eₙ; then define for ε > 0 and x ∈ X the thresholding approximations as , where . We study a generalized version of that we call the weak thresholding approximation. We modify the in the following way. For ε > 0, t ∈ (0,1) we set and consider...
I. Assani (2005)
Colloquium Mathematicae
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We answer a question of H. Furstenberg on the pointwise convergence of the averages , where U and R are positive operators. We also study the pointwise convergence of the averages when T and S are measure preserving transformations.
Péter Kórus, Ferenc Móricz (2010)
Studia Mathematica
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We investigate the convergence behavior of the family of double sine integrals of the form , where (u,v) ∈ ℝ²₊:= ℝ₊ × ℝ₊, ℝ₊:= (0,∞), and f: ℝ²₊ → ℂ is a locally absolutely continuous function satisfying certain generalized monotonicity conditions. We give sufficient conditions for the uniform convergence of the remainder integrals to zero in (u,v) ∈ ℝ²₊ as maxa₁,a₂ → ∞ and , j = 1,2 (called uniform convergence in the regular sense). This implies the uniform convergence of the partial...
Sreela Gangopadhyay (1990)
Colloquium Mathematicae
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Ferenc Móricz (2005)
Colloquium Mathematicae
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The concepts of statistical convergence of single and double sequences of complex numbers were introduced in [1] and [7], respectively. In this paper, we introduce the concept indicated in the title. A double sequence is said to be regularly statistically convergent if (i) the double sequence is statistically convergent to some ξ ∈ ℂ, (ii) the single sequence is statistically convergent to some for each fixed j ∈ ℕ ∖ ₁, (iii) the single sequence is statistically convergent...
S. V. Konyagin, V. N. Temlyakov (2003)
Studia Mathematica
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We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in...
Laure Dumaz, Bálint Virág (2013)
Annales de l'I.H.P. Probabilités et statistiques
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The Tracy–Widom distribution is the large dimensional limit of the top eigenvalue of random matrix ensembles. We use the stochastic Airy operator representation to show that as the tail of the Tracy–Widom distribution satisfies
Larry Kitchens, Charles Swartz (1974)
Colloquium Mathematicae
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Adam Osękowski (2016)
Colloquium Mathematicae
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Let N ≥ 2 be a given integer. Suppose that is a martingale difference sequence with values in and let be a deterministic sequence of signs. The paper contains the proof of the estimate . It is shown that this result is asymptotically sharp in the sense that the least constant in the above estimate satisfies . The novelty in the proof is the explicit verification of the ζ-convexity of the space .
Z. Sadlok, Z. Tyc (1977)
Annales Polonici Mathematici
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Donald E. Myers (1976)
Annales Polonici Mathematici
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David Brink (2015)
Acta Arithmetica
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We show how the idea behind a formula for π discovered by the Indian mathematician and astronomer Nilakantha (1445-1545) can be developed into a general series acceleration technique which, when applied to the Gregory-Leibniz series, gives the formula with convergence as , in much the same way as the Euler transformation gives with convergence as . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in...
Grażyna Anioł (2006)
Bollettino dell'Unione Matematica Italiana
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For bounded functions on an interval , in particular, for functions of bounded p-th power variation on there is estimated the rate of pointwise convergence of the Bezier-type modification of the discrete Feller operators. In the main theorem the Chanturiya modulus of variation is used.
Hans-Peter Blatt (2015)
Banach Center Publications
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Let f be meromorphic on the compact set E ⊂ C with maximal Green domain of meromorphy , ρ(f) < ∞. We investigate rational approximants of f on E with numerator degree ≤ n and denominator degree ≤ mₙ. We show that a geometric convergence rate of order on E implies uniform maximal convergence in m₁-measure inside if mₙ = o(n/log n) as n → ∞. If mₙ = o(n), n → ∞, then maximal convergence in capacity inside can be proved at least for a subsequence Λ ⊂ ℕ. Moreover, an analogue...
Harman Preet Singh Kapoor, Kanchan Jain (2011)
Discussiones Mathematicae Probability and Statistics
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For any insurance contract to be mutually advantageous to the insurer and the insured, premium setting is an important task for an actuary. The maximum premium ( that an insured is willing to pay can be determined using utility theory. The main focus of this paper is to determine by considering different forms of the utility function. The loss random variable is assumed to follow different Statistical distributions viz Gamma, Beta, Exponential, Pareto, Weibull, Lognormal and Burr....
Urban Cegrell (2007)
Annales Polonici Mathematici
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We show that if a decreasing sequence of subharmonic functions converges to a function in then the convergence is in .
Eve Oja, Silja Treialt (2013)
Studia Mathematica
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The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair has the λ-bounded approximation property. Then there exists a net of finite-rank operators on X such that and for all α, and and converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.
Abraham Racca, Emmanuel Cabral (2016)
Mathematica Bohemica
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Equiintegrability in a compact interval may be defined as a uniform integrability property that involves both the integrand and the corresponding primitive . The pointwise convergence of the integrands to some and the equiintegrability of the functions together imply that is also integrable with primitive and that the primitives converge uniformly to . In this paper, another uniform integrability property called uniform double Lusin condition introduced in the papers...
Harry I. Miller (2007)
Bollettino dell'Unione Matematica Italiana
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The concept of statistical convergence of a sequence was first introduced by H. Fast [7] in 1951. Recently, in the literature, the concept of statistical convergence of double sequences has been studied. The main result in this paper is a theorem that gives meaning to the statement: converges statistically to if and only if "most" of the "subsequences" of converge to in the ordinary sense. The results presented here are analogue of theorems in [12], [13] and [6] and are concerned...
Alain Faisant, Georges Grekos, Ladislav Mišík (2016)
Mathematica Bohemica
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Let be a convergent series of positive real numbers. L. Olivier proved that if the sequence is non-increasing, then . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the -convergence, that is a convergence according to an ideal of subsets of . Again, Olivier’s theorem is a consequence...
Maria Deijfen, Remco van der Hofstad, Gerard Hooghiemstra (2013)
Annales de l'I.H.P. Probabilités et statistiques
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We formulate and study a model for inhomogeneous long-range percolation on . Each vertex is assigned a non-negative weight , where are i.i.d. random variables. Conditionally on the weights, and given two parameters , the edges are independent and the probability that there is an edge between and is given by . The parameter is the percolation parameter, while describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether...
Benedetta Noris, Hugo Tavares, Susanna Terracini, Gianmaria Verzini (2012)
Journal of the European Mathematical Society
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In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system , as the interspecies scattering length goes to . For this system we consider the associated energy functionals , with -mass constraints, which limit (as ) is strongly irregular. For such functionals, we construct multiple critical points...
Boaz Tsaban, Lubomyr Zdomsky (2012)
Journal of the European Mathematical Society
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A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii spaces, for which every sheaf at a point can be amalgamated in a natural way. Let denote the space of continuous real-valued functions on with the topology of pointwise convergence. Our...